Information Aggregation of Group Decision Making in Emergency Events

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doi:10.4236/iim.2010.28057 Published Online August 2010 (http://www.SciRP.org/journal/iim)

Information Aggregation of Group Decision-Making in

Emergency Events

*

Kefan Xie, Qian Wu, Gang Chen, Chao Ji

Management school, Wuhan University of Technology, Wuhan, China

E-mail: xkf@whut.edu.cn, shashavio@sohu.com,{cg224, jichaowuqiao2003}@163.com Received May 14, 2010; revised June 22, 2010; accepted July 19, 2010

Abstract

Information is a key factor in emergency management, which helps decision makers to make effective deci-sions. In this paper, aiming at clarifying the information aggregation laws, and according to the characteristic of emergency information, information relative entropy is applied in the information aggregation to establish the information aggregation model of emergency group decision-making. The analysis shows that support and credibility of decision rule are the two factors in information aggregation. The results of four emergency decision-making groups in case study support the analysis in the paper.

Keywords:Emergency, Group Decision-Making, Information Aggregation, Relative Entropy

1. Introduction

As an important part of the emergency management, decision-making system for emergency response is one of the most important research areas. Emergency deci-sion-making is a group decideci-sion-making process. Emer-gency managers make decision in the situation of con-straint time, incomplete and inaccurate information. They brainstorm and coordinate the interests of multiple deci-sion-makers, in order to handle variety of emergency for achieving timely, effective and smooth goal. Group deci-sion-making behavior in emergency management attracts more and more attention of the whole society.

When making decisions on complex issues, in order to scientific decision-making and avoid individual subjec-tive judgments, choice and preference impact on the de-cision results, emergency managers should analysis, judgment and decision by adopting integrated experience and wisdom of expert groups and method of group deci-sion-making. Information aggregation has a significant effect in the process of group decision-making, which be-comes a hot topic on the emergency management research.

According to information aggregation research, Ame- rican scholar Yager [1] proposes Ordered Weighted Av-eraging Operator. Bodily [2] gives information aggrega-tion method based on principal process. Brock [3] puts forward information aggregation method based on Nash- Harsanyi negotiation model. Krzyszto and Duck [4] propose the information aggregation on the basis of group

value judgment. Chen Dongfeng et al. [5] make an uni-formization of four common preference information given by decision makers, which are real value, interval values, language phrases and intuitionistic fuzzy value, based on conversion of formula between deferent fuzzy preference information. Li Bingjun and Liu Sifeng [6] construct a defining-number judgment matrix of certain credibility which is equivalent to group information of interval number reciprocal judgment matrix based on-set-valued statistics principle. Wu Jiang and Huang Dengshi [7] construct the relation functions based on four interval number preference information, namely interval number preference orderings, interval number utility values, interval number complementary judgment matrices and interval number reciprocal judgment matri-ces, which uniforms different uncertain preference in-formation. Zhou Shizhong et al. [8]analysis characteris-tics of four kinds uncertain preference and propose a goal programming model to aggregate the group preference. Zhu Jianjun [9] studies the group aggregation approach of interval number reciprocal comparison matrix and interval number complementary comparison matrix by using UOWA method. Feng Xiangqian et al. [10] con-struct an aggregating of interval number judgment ma-trixes with maximum satisfaction. Guiwu Wei [11] pro-poses intuitionistic fuzzy ordered weighted geometric operator and interval-valued intuitionistic fuzzy ordered weighted geometric operator to study multiple attribute group decision making issue. H. J. Zimmermann and P. Zysno [12]representing the criteria (subjective categories)

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by fuzzy sets which is possible to use aggregation op-erators as models for the amalgamation of those criteria. Xie Kefan and Chen Gang [13] research on the entre-preneurial Team’s Risk Decision-Making Process Based on Group Learning.

In short, most scholars have focused on the various structural preference aggregation methods. However, the information aggregation has been little studied in emer-gency cases.

2. Information Aggregation Mechanism of

Group Decision-Making in Emergency

Management

Whether emergency decision making is a scientific deci-sion, depends on whether there is a consistence between quality of information and preference information of expert decision-making. Quality of decision-making in-formation is critical to the ways of group decision-making. Quality of decision-making information refers to the authenticity and credibility of the information. Informa-tion aggregaInforma-tion refers to the process of gathering, com-pressing, screening, refining and integrating to decision- making information, which includes aggregation to deci-sion-making information and aggregation to expert pref-erence information. Aggregation to decision-making information composes of information awareness and screening.

Information aggregation of group decision-making in emergency management has two characteristics as follow: 1) Emergency decision-making actors are large groups, which are collections of various groups. Therefore, in-formation aggregation among groups should be taken into account when study on group decision-making; 2) There are two factors to be considered in group decision- making: statutory decision-making power and expert deci-sion-making power. Statutory decideci-sion-making power is mainly used in emergency decision-making mechanism, and expert decision-making power is mainly used in credibility and support of expert decision-making.

2.1. Information Perception

After the outbreak of unexpected events, the interests of all groups would like to obtain the original information as much as possible to make a scientific decision-making to respond to emergency in order to protect their own interests, reduce the loss of harm. Information perception is the first act of information aggregation stage, which refers to the process of getting information by interest groups through various channels and means. The amount of information increases exponentially and generates information associated with variation and deviation after the outbreak of unexpected events, which may bring a lot

of information garbage. The information in this stage is incompleteness, and transmission route owns of charac-teristics of plurality, asymmetry and mutagenicity etc. In this stage, information aggregation of interest groups reflects in the “quantity”, which means that obtaining information the more the better and as soon as possible.

2.2. Information Screening

Information screening is the second stage of information aggregation. Information screening refers to information process of screening, identification, verification of its authenticity, validity to the first stage perceptible infor-mation through various technical means which based on laws and rigorous, serious, scientific workflow. Informa-tion screening includes two parts of informaInforma-tion process control and information content control. Information screening is the screening authenticity of information in essence in order to ensure the validity of the information. At this stage, each group pays more attention to false, unrealistic and not useful information. After screening the authenticity and validity of information greatly in-creased and becomes an important basis for group deci-sion-making. Information screening methods can be summarized into two parts. On the one hand it can be judged by perceptions and experiences of decision mak-ers; on the other hand, it can be judged by analyzing, summarizing and organizing the various historical data of past emergency events to find all kinds of information regularity. Information aggregation at this stage of in-formation gathering reflected in the “quality”, which means that the more real the obtained information, the better the efficiency will be.

2.3. Preference Information Aggregation

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mmarized into four types, interval preference order, in-terval utility value, inin-terval number reciprocal compari-son matrix and interval number complementary com-parison matrix. Currently, the main methods to synthesis expert opinion and preference in group decision-making can be divided into two categories: Comprehensive Judgment Matrix and Comprehensive sequencing vector. Preference information aggregation is a method of deci-sion makers to take some form of the above or any par-ticular form of individual preferences for the group pref-erence aggregation process. However, the However, the different structure of preference information of the proc-ess the same information to generate distortion is inevi-table, how to ensure the validity of the information would be an important issue.

3. Information Relative Entropy

Aggregation Model of Group

Decision-Making in Emergency Events

3.1. Model Assumes

1) In the process of decision-making in emergency man-agement, assuming that n groups decision of the emergency response form

n

decision table. Suppose

T is decision table setTj



U Cj, 

 

d



,j1, 2, , n,



1, , ,2 n



T  T T T , where decision table

T

_j of certain group

j

corresponds to mjdecision-making rule, any

of which



 

_{ }

 

_{ }



ij ij

ij ij C d

R u  rule des x  des x has

support SDij and credibility CDij;

Then _{ } ij ij

ij C d j

S D  x _ U (1)

   

i j i j i j

i j C d C

C D  x _ x (2)

2) In the process of decision-making in emergency management, there are communication and games among all the groups, which can aggregate m decision rule of group, where any decision-making rule Ruiof group has

supportSDiand credibilityCDi.

3) In the process of decision-making in emergency management, assuming that any group weight is



_j, then, group decision-making weight distribution is



1, 2, , j, , n



     .

Theorem 1: The number of group decision rule

m

is greater than or equal to the number of any group deci-sion-making rule mjin group, that is mjm.

Certification: Assuming that mj decision rules of

group j can form decision-making system of Sj 

 



U Cj,  d



. Therefore, in the decision-making system,

if x x1j, 2jUjas well as x2j  x1j_C , then it is inevitable that ₂_j ₁_j

d

x _{  }x  , that is the decision system

is incompatible, and there are mj decision rules to meet

the conditions. Assume that group decision-making sys-tem is S 



U C, 

 

d



, then Sj S is inevitable.

Assuming that S S j is one of decision-making system,

if   x U U_j,  x_j U_j as well as x_{  } x_{j C},

j d

x_{  } x , then group decision-making system S

 



U C,  d



is incompatible and there are more than

1 j

m  decision rules to meet the condition, that is

1

j j

m m  m ; If   x U U_j,  x_j U_j as well as

,

j _C j _d

x _{ }x x _{ }x , then decision-making system

j

S S and Sj



U Cj, 

 

d



is fully compatible, but

there are at least m_j decision-making rules, that is

j

m m , so m_jm.

3.2. Support and Credibility of Decision Rule

For m_j m, group

j

in the decision-making gruops may not has the whole decision-making rule which groups possesses, that is parts of the decision rule are not owned by group

j

, which is called loss of deci-sion-making rule. If there is a decideci-sion-making rule

 

 

 



i i



i i C d

Ru  rule des x des x in group, any one decision-making rule



 

 

ij

ij ij C

Ru  rule des x

 

 

dij



des x

 of certain one group j does not satisfy the conditions:

 

_{ }

 

_{ }

ij i

C C

des x des x and des x

 

 

d_ij

 

 

di

des x

 , then, decision-making rule

Ru

_i is an

loss decision rule for group j. According to the formula (1) and (2), the support and credibility of decision rule are SDij 0 and CDij 0. However, certain support

and credibility of decision-making rules is essentially not Zero. For example, when

 

_{ }

 

_{ }

ij i

C C

(4)

and

 

_{ }

 

_{ }

ij i

d d

des x des x  , the support and

credi-bility of decision rule losses do not always equals Zero. Therefore, the amount of support and credibility of deci-sion-making rule loss should depend upon the state of affair.

1) If group j has one decision-making ruleRuij

which can contain loss decision-making ruleRu_i, and satisfies the condition of _{ }



_{ }



' i

i j

C C

d es_ x  _ d es x

  and

 

 

d_ij

 

 

d_i

des x des x , then the support and credibility

of loss decision-making ruleRui is in accordance with

the support and credibility of decision-making ruleRu_{i j}' ,

that is SDij SD_{i j}' , CDij CD_{i j}' . For the purpose of

group j , if there are _m' _{decision-making rule}

'

i j

Ru which can contain the loss decision-making ruleRui, then the support and credibility of loss

deci-sion-making rule Ruiare as follow:

'

' ' ₁

m

ij _{i j}

i

SD SD





，

'

' ' ₁

m

ij _{i j}

i

CD CD





(3)

2) If group j has one decision-making rule Ruij

which satisfies the condition of

 

'

i j

C

des x_  _ des

 

 

 

x Ci and des x

 

 

dij des x

 

 

di  , and the

de-cision-making rule Ru_{i j}' is restrict and incompatible to

the loss decision-making rule Ru_i, then the support and credibility of loss decision-making rule Rui are:

0 ij

SD  ，CDij0 (4)

3) If group j has no decision-making ruleRu_ij

which satisfies the condition of

 

'

i j

C

des x_  _ des

 

 

 

x Ci , des x

 

 

dij des x

 

 

di or des x

 

 

dij des

 

 

xdi  , then the loss decision-making rule is not

relevant to the Ruij, that is in the condition of

 

_'

i j C

x

_,

group j has neither decision nor strategy, which is re-garded as abstention in decision-making process. There-fore, the support and credibility of those kinds of loss decision-making rules to group j, are in accordance with emergency decision-making mechanism. Assuming to the above, the support and credibility of decision-making

strategy to abstention in emergency decision-making process are meeting the condition as follow:

0

ij

SD  , 0CDij  (5)

3.3. Decision-Making Weight

In the emergency response decision-making process, a number of factors influence the decision-making groups in decision weights, in which legal decision-making weight and expert decision-making weight are the two main factors. The mechanism of group decision-making to the legal decision-making weight is related with emergency decision-making mechanism; the mechanism of group decision-making to the expert decision-making weight is related with the credibility of expert groups. Those two weight response the emergency decision- making process, and demonstrate the laws of the follow-ing points:

1) The strategies of expert decision-making groups have more credibility and less ambiguous decision. The expert credibility enhances the decision-making weight of expert decision-making groups. The less ambiguous decision shows that there is less flexibility but more rigid in the decision-making, resulting in the more firm weight.

2) No matter how big groups of legal decision-making power, when it has ambiguous type of strategy and more decision-making room, legal decision-making weight will be greatly reduced. In order to meet decision-making target, decision makers may randomly adjust their strat-egy in order to influence their decision-making weight.

Therefore, in the process of emergency decision-making, group decision-making weight is in accordance with credibility of decision-making strategy. The more the credibility, the higher the decision-making weight, the less the credibility, the lower the decision-making weight. Hence, assuming that decision-making weightij of

group j in decision strategyRu_ij is proportionate to credibility CD_ij of the decision-making rule. Deci-sion-making weight_ijof group j in decision strategy

ij

Ru can be represented by the relative credibility of decision-making ruleRu_ijto group j:

1 1

n n

ij ij ij ij ij

j j

e e CD CD



 









(6)

(5)

1

m

j ij ij

i

e  SD





 (7) After normalization of decision-making weight to each decision-making group in the group, it is available to get decision weights of the groups:



1, 2, , n



    , and

1 j j n j j e e   



(8)

3.4. Model of Information Relative Entropy Aggregation

In process of emergency group decision-making, in order to obtain more efficient decision strategy, every group in the group want to choose the minimized deviation values of decision-making rules according to group decision- making rule. Therefore, the support SDiof group

deci-sion-making ruleRuican be computed by relative

en-tropy aggregation model as Equation (9).

Where _j in (9) is the decision-making weight of group

j

, which can be computed by (8).

With nonlinear programming (9), local optimal solu-tion *



* * *



1, 2, ,

T m

SD  SD SD  SD can be calculated,

where *

 

1

1 1

, 1, 2, ,

j j

n m n i ij ij

i

j j

SD b  b  i m



 









  , and

1

m

ij ij ij

i

b SD SD





.

In the process of emergency group decision-making,

 

 

 



i i



i i C d

Ru  rule des x des x is one of group

decision-making rules, where group credibility is CDi.

If __m*_{decision-making rule meet the conditions as}

follows: *



*

 

 

*

 

 

*



i i

i i C d

Ru  rule des x  des x and

 

 

*

i

C

des x 

 

 

,

 

 

*

 

 

i i i

C d d

des x des x des x , and assuming that credibility of any decision-making rule *

i

Ru to group

j

is CD_{i j}* . Then, credibility CDi

of any decision-making rule *

i

Ru can be calculated by relative entropy aggregation model (10) as follows:

Wherej in (10) is the decision-making weight of

group

j

, which can be computed by (8).

With nonlinear programming (10), local optimal

solu-tion



*



* * * *

1, 2, ,

T

m

CD  CD CD  CD can be calculated,

where *

_{ }

*

_{ }

*

1

1 1

, 1, 2, ,

j j

n m n i ij ij

i

j j

CD c  c  i m



 



_

_

_

  , and

*

1

m

ij ij ij

i

b SD SD





.

From (9) and (10) it is known that SDij 0 and 0

ij

CD  is not in conformity with the two kinds of de-cision-making loss situation, that is, in the situation of decision-making rule loss, support and credibility of group decision-making rule cannot be calculated by (9) and (10). To circumvent this problem, it is better to make infinitesimal positive real numbers to support and credi-bility of loss decision-making rule in decision-making rule loss situation as follows:   0 and  0, let

ij ij

SD CD .

4. Case Study

In the process of emergency decision-making, there are









1 1

1

m in lo g lo g

. . 1

n m

ij

j i i m

j i ij i m i i S D

S D S D S D

S D

s t S D

                             _ _ __       



(9)





*





* * 1 1 1 1

min log log

. . 1

n m

ij

j i i _m

j i ij i m i i C D

C D CD CD

C D

s t C D

(6)

[image:6.595.56.543.97.279.2]

Table 1. Decision-making table T1.

Decision-making rules style Position Type Decision CD SD

1

 Y S D accept 75.00% 9.09%

2

 Y S D reject 25.00% 3.03%

3

 Y J D accept 50.00% 9.09%

4

 Y J D reject 50.00% 9.09%

5

 Y J X accept 33.33% 6.06%

6

 Y J X reject 66.67% 12.12%

8

 P S D reject 100.00% 9.09%

9

 P S X accept 100.00% 3.03%

11

 P J D accept 100.00% 27.27%

13

 P J X accept 75.00% 9.09%

14

[image:6.595.60.540.310.478.2]

 P J X reject 25.00% 3.03%

1

 Y S D accept 100.00% 20.59%

3

 Y J D accept 71.43% 14.71%

4

 Y J D reject 28.57% 5.88%

5

 Y J X accept 100.00% 2.94%

10

 P S X reject 100.00% 8.82%

11

 P J D accept 25.00% 2.94%

12

 P J D reject 75.00% 8.82%

14

 P J X reject 100.00% 5.88%

15

 Y S X accept 90.00% 26.47%

16

 Y S X reject 10.00% 2.94%

1

 Y S D accept 85.71% 14.29%

2

 Y S D reject 14.29% 2.38%

3

 Y J D accept 50.00% 4.76%

4

 Y J D reject 50.00% 4.76%

5

 Y J X accept 50.00% 7.14%

6

 Y J X reject 50.00% 7.14%

7

 P S D accept 25.00% 2.38%

8

 P S D reject 75.00% 7.14%

12

 P J D reject 100.00% 9.52%

13

 P J X accept 85.71% 14.29%

14

 P J X reject 14.29% 2.38%

15

 Y S X accept 90.00% 21.43%

16

[image:6.595.56.540.511.723.2]

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four groups in the decision-making group, and the decision-making rules of the four groups are respectively listed in Tables 1-4. According to the four deci-sion-making tables we can find that the four groups con- stituting a group have 15 decision-making rules, which are  1, 2, ,15 respectively. The four groups all have

decision-making loss in parts of their decision, therefore the support and credibility of four groups loss deci sion-making can be calculated by model (3),(4) and (5). According to model (6), (7) and (8), the results of decision

making weight of four groups are 0.301, 0.239, 0.213, 0.247, respectively. Due to the fact that parts of support and credibility of loss decision-making are Zero, it in-fluences the results of support and credibility of deci-sion-making to the groups by using model (9) and (10). In order to eliminate this impact, we define that support and credibility of loss decision-making rule are alternated by ₁₀6_{. The results are shown in}_{Table 5}_{as follows:}

[image:7.595.47.540.227.407.2]

According to Table 5, after aggregating by relative entropy, the support and credibility of group decision-

1

 Y S D accept 28.57% 5.71%

2

 Y S D reject 71.43% 14.29%

3

 Y J D accept 25.00% 2.86%

4

 Y J D reject 75.00% 8.57%

5

 Y J X accept 50.00% 5.71%

6

 Y J X reject 50.00% 5.71%

9

 P S X accept 16.67% 2.86%

10

 P S X reject 83.33% 14.29%

12

 P J D reject 100.00% 8.57%

13

 P J X accept 100.00% 11.43%

15

 Y S X accept 100.00% 20.00%

Table 5. The group decision-making rules.

1

j j2 j3 j4

0.301 0.239 0.213 0.247 group

Decision- making

rules

1

i

CD SD_i₁ CD_i₂ SD_i₂ CD_i₃ SD_i₃ CD_i₄ SD_i₄ CD_i SD_i

1

 75.00% 9.09% 100.00% 20.59% 85.71% 14.29% 28.57% 5.71% 97.79% 33.26%

2

 25.00% 3.03% 0% 0% 14.29% 2.38% 71.43% 14.29% 2.21% 1.10%

3

 50.00% 9.09% 71.43% 14.71% 50.00% 4.76% 25.00% 2.86% 48.69% 20.48%

4

 50.00% 9.09% 28.57% 5.88% 50.00% 4.76% 75.00% 8.57% 51.31% 21.57%

5

 33.33% 6.06% 100.00% 2.94% 50.00% 7.14% 50.00% 5.71% 95.66% 15.95%

6

 66.67% 12.12% 0% 0% 50.00% 7.14% 50.00% 5.71% 4.34% 1.68%

7

 0% 0% 0% 0% 25.00% 2.38% 0% 0% 1.22% 0.00%

8

 100.00% 9.09% 0% 0% 75.00% 7.14% 0% 0% 98.78% 0.10%

9

 100.00% 3.03% 0% 0% 0% 0% 16.67% 2.86% 61.34% 0.09%

10

 0% 0% 100.00% 8.82% 0% 0% 83.33% 14.29% 38.66% 0.09%

11

 100.00% 27.27% 25.00% 2.94% 0% 0% 0% 0% 7.93% 0.16%

12

 0% 0% 75.00% 8.82% 100.00% 9.52% 100.00% 8.57% 92.07% 0.88%

13

 75.00% 9.09% 0% 0% 85.71% 14.29% 100.00% 11.43% 69.49% 2.12%

14

 25.00% 3.03% 100.00% 5.88% 14.29% 2.38% 0% 0% 30.51% 0.81%

15

 0% 0% 90.00% 26.47% 90.00% 21.43% 100.00% 20.00% 98.79% 1.68%

16

 0% 0% 10.00% 2.94% 10.00% 2.38% 0% 0% 1.21% 0.03%

[image:7.595.60.538.434.720.2]

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making rule change both. The support of decision-making 1 is greatest, and its result is 33.26%. The reason

why it support is so high is because that supports of any groups in group to the decision-making rules are high, and the groups have higher degree of recognition accep-tance. However, the support of decision-making 7 is

lowest, and its result is 0.003%. The reason why it sup-port is so low is because that recognitions of the deci-sion-making rule in group lacks of consensus, and it only support by group j3 but its support is just 2.38%. The credibility of decision-making rule 8 is greatest

to group and its result is 98.78%. Though group lacks of consensus in recognition to the decision-making rule, two groups j1 and j3 in decision-making groups have high support, even to a firm degree. The credibility of decision-making rule₇and₁₆is lowest to groups and their results are 1.22% and 1.21%. The reason of low credibility in 7 is that there is lacking of consensus in

groups. The reason of low credibility in 16is that there

is lacking of consensus in groups as well as believing that credibility of group is low in decision-making rule. The analysis result shows that group decision aggrega-tion by relative entropy is feasible, scientific and reliable.

5. Conclusions

In the process of group decision-making in emergency management, information plays an important role to make effect decision strategies. This paper analyzes the information aggregation mechanism by using informa-tion relative entropy method, and believes that the law of information aggregation can be found out according to the information aggregation model.

6. References

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